Conditional Random Sample in R

I am wondering what the best way to solve this is. Essentially I want to generate 20 samples which add to 100 but also where (x1+x2>20). I am struggling to get something that is fast and efficient. I realise that I could filter out the lines that don't meet this criteria but it isn't efficient if I generate 10,000 rather than 20.

The code is as below:

n = 20
x1 = sample(0:100,n,replace = TRUE)
x2 = sample(0:100,n,replace = TRUE)
x3 = sample(0:100,n,replace = TRUE)
index = (x1+x2+x3)>100
G=(x1+x2)>20
while(sum(index)>0&&sum(G)>0){
   x1[index&&G] = sample(0:100,n,replace = TRUE)
   x2[index&&G] = sample(0:100,n,replace = TRUE)
   x3[index&&G] = sample(0:100,n,replace = TRUE)
index =(x1+x2+x3)>100
G=(x1+x2)>20
}
x4=rep(100,n)-x1-x2-x3

df <- data.frame(x1,x2,x3,x4)

Thanks in advance.